Problem with matrices question, finding A^2

**DaveWolfgang** · July 15th 2012, 10:21 AM

The question is this one below:

Let
A =
(1 -3)
2 0

How am I supposed to find A^2?

Also Let
B =
(-6 3 )
8 20

How do I find Matrix X such that 5X-A=B ?

Full explanations would be nice, someone tried to explain it to me briefly but I didn't quite understand it.

**Reckoner** · July 15th 2012, 11:55 AM

Originally Posted by DaveWolfgang

How am I supposed to find A^2?

$A^2 = A\cdot A = \left[\begin{array}{cc}1&-3\\2&0\end{array}\right]\cdot\left[\begin{array}{cc}1&-3\\2&0\end{array}\right]$

Originally Posted by DaveWolfgang

How do I find Matrix X such that 5X-A=B ?

You know that $X$ has to be a 2×2 matrix for the subtraction to be valid. If we let

$X = \left[\begin{array}{cc}a&b\\c&d\end{array}\right],$

then

$5X - A = B$

$\Rightarrow5\left[\begin{array}{cc}a&b\\c&d\end{array}\right] - \left[\begin{array}{cc}1&-3\\2&0\end{array}\right] = \left[\begin{array}{cc}-6&3\\8&20\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}5a-1&5b+3\\5c-2&5d\end{array}\right] = \left[\begin{array}{cc}-6&3\\8&20\end{array}\right]$

Now equate the corresponding entries.

**emakarov** · July 15th 2012, 12:08 PM

Originally Posted by DaveWolfgang

How do I find Matrix X such that 5X-A=B ?

Or just X = (1/5)(B + A).

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